I am foreign-born and speak with a strong accent, too. I was treated very badly because of that many times. Unfortunately, language discrimination, just as plain good 'old rasism, can be a reality among nurses.
No one, ever, has right to make conclusion about your ability as a professional because of your accent. Refuse placement with this so-called "nurse" in the future. If necessary, speak with your Dean ASAP. You have right to demand other placement if you feel discriminated against. Do not spend money on "accent reduction" - nobody in the right mind would recommend that denigrating and humiliating "education" for someone born in Tupelo, Mississippi and moving to Boston, MA, so you shouldn't do it, too.
For your future job search
, seek places where there are other foreign-born or Spanish-speaking nurses or choose facilities which serve a lot of Spanish-speaking patients. You'll be in high demand there. Best of luck!